Negative thermal expansion and magnetoelastic coupling in the breathing pyrochlore lattice material ${\mathrm{LiGaCr}}_4{\mathrm{S}}_8$

The physical properties of the spinel ${\mathrm{LiGaCr}}_4{\mathrm{S}}_8$ have been studied with neutron diffraction, x-ray diffraction, magnetic susceptibility, and heat capacity measurements. The neutron diffraction and synchrotron x-ray diffraction data reveal negative thermal expansion (NTE) below 111(4) K. The magnetic susceptibility deviates from Curie-Weiss behavior with the onset of NTE. At low temperature a broad peak in the magnetic susceptibility at 10.3(3) K is accompanied by the return of normal thermal expansion. First-principles calculations find a strong coupling between the lattice and the simulated magnetic ground state. These results indicate strong magnetoelastic coupling in ${\mathrm{LiGaCr}}_4{\mathrm{S}}_8$.

Figure 1

Crystal structure of ${\mathrm{LiGaCr}}_4{\mathrm{S}}_8$ depicting the breathing pyrochlore Cr sublattice. The exchange interactions within the small and large tetrahedra are labeled $J_1$ and $J_1^{\prime }$, respectively. $J_2$ denotes the next nearest neighbor exchange interaction.

Figure 2

(a) Synchrotron x-ray diffraction data with $\lambda =0.4146\AA$ collected at 300 K. The inset displays a limited region of reciprocal space so that the presence of a weak ${\mathrm{Cr}}_3{\mathrm{S}}_4$ can be compared to the intensity of the main phase. The impurity phase is indicated by arrows. The axis labels are the same as the main panel, but note the logarithmic $y$-axis scale. Neutron diffraction data collected with POWGEN with 0.167 $\le \lambda \le 1.233 \AA$ at 300 K and 1.5 K are shown in panels (b) and (c), respectively. The Rietveld refinement of the structural model described in the text with space group $F\overline{4}3m$ is indicated by the solid line through the data.

Figure 3

Lattice parameter of ${\mathrm{LiGaCr}}_4{\mathrm{S}}_8$ as a function of temperature obtained by neutron diffraction. Negative thermal expansion is observed below 111(4) K. The inset shows the estimated temperature dependence of $\mathrm{\Delta }a\left(T\right)/a_0$ determined as explained in the text.

Figure 4

Temperature dependence of peak width (full width at half maximum of a standard Lorentzian function) of selected diffraction peaks determined from the laboratory x-ray diffraction data. All peaks broaden with cooling at low temperature.

Figure 5

Temperature-dependent Cr-Cr bond lengths in the small and large ${\mathrm{Cr}}_4$ tetrahedra (filled squares, left scale) and $B_r$ (filled circles, right scale). These bond lengths and $B_r\mathrm{s}$ are obtained from the neutron diffraction data collected with POWGEN.

Figure 6

Variation of selected bond angles with temperature in ${\mathrm{LiGaCr}}_4{\mathrm{S}}_8$. Cr-S-Cr bonds are close to ${90}^{\circ }$ and are responsible for the NN superexchange interaction. S-Li-S and S-Ga-S bonds are insensitive to the change in temperature whereas other bonds show a weak anomaly with the onset of NTE.

Figure 7

Magnetic susceptibility measurements of ${\mathrm{LiGaCr}}_4{\mathrm{S}}_8$. (a), (b) Show the temperature-dependent dc susceptibility, $\chi$, and (c) shows the temperature-dependent inverse dc susceptibility, $1/\chi$, of ${\mathrm{LiGaCr}}_4{\mathrm{S}}_8$. (d) Displays the in-phase part of the ac susceptibility, ${\chi }^{\prime }$, around the magnetic transition, measured with ${\mathit{H}}_{\mathit{ac}}=5$ Oe with frequencies 29 Hz, 127 Hz, 1129 Hz, 2336 Hz, 4832 Hz, and 10 000 Hz. The arrow in (d) indicates the direction of increasing applied frequency. The inset of (c) displays $M\left(H\right)$ loops measured at selected temperatures. A peak in the susceptibility occurs at 10.3(3) K and deviation from Curie-Weiss behavior is observed below 110 K. A small shift in the peak of ${\chi }^{\prime }$ towards higher temperature is noticed with the increase in frequency. Weak hysteresis in the $M$ vs $H$ data is observed at 3 K.

Figure 8

Temperature-dependent heat capacity, ${\mathit{C}}_{\mathit{P}}$, of ${\mathrm{LiGaCr}}_4{\mathrm{S}}_8$ at zero magnetic field. (a) Displays the ${\mathit{C}}_{\mathit{P}}$ from 2 to 200 K. (b) Shows ${\mathit{C}}_{\mathit{P}}/T$ and the estimated entropy, $S$, at low temperatures. The theoretical value of magnetic entropy for the spin-3/2 system is indicated by the horizontal line in (b). The change in slope of ${\mathit{C}}_{\mathit{P}}$ around at 120 K and a broad hump at 10.9(4) K look coincident with the bounding temperatures of NTE.

Figure 9

Temperature-dependent resistivity, $\rho$, of ${\mathrm{LiGaCr}}_4{\mathrm{S}}_8$. The fitting function is described in the text.